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30 August, 02:33

One heater uses 310 W of power when connected by itself to a battery. Another heater uses 180 W of power when connected by itself to the same battery. How much total power do the heaters use when they are both connected in series across the battery?

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Answers (2)
  1. 30 August, 02:35
    0
    Given:

    Heater 1:

    Power, P1 = 310 W

    Heater 2:

    Power, P2 = 180 W

    Power, P = I^2 * R

    Equivalent resistance in series, Req

    Req = R1 + R2

    Where,

    R1 = resistance in heater 1

    R2 = resistance in heater 2

    Total Power, Pt = V^2 * Req

    Since they were connected to the same battery of voltage, V. In series connection,

    = P1 + P2

    P1 = V^2/R1

    Req = V^2/P

    = V^2/310 + V^2/180

    1/Pt = (1/310 + 1/180)

    = 0.0087814

    Pt = 113.88 W
  2. 30 August, 02:38
    0
    55.8W

    Explanation:

    P = V^2/R

    R = V^2/P

    For series connection

    Req = R1 + R2 = V^2/310 + V^2/180

    R=V^2/P = V^2/310 + V^2/180

    But V^2 will cancel out

    P = 1 / (1/310 + 1/180)

    P = 55.8W
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